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Scaling limits of recurrent excited random walks on integers

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Scaling limits of recurrent excited random walks on integers
2.	Creator	Author's name, affiliation, country	Dmitry Dolgopyat; University of Maryland; United States
2.	Creator	Author's name, affiliation, country	Elena Kosygina; Baruch College and the CUNY Graduate Center; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	excited random walk; cookie walk; branching process; random environment; perturbed Brownian motion
3.	Subject	Subject classification	60K37; 60F17; 60G50
4.	Description	Abstract	We describe scaling limits of recurrent excited random walks (ERWs) on $\mathbb{Z}$ in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations. It is known that ERW is recurrent if and only if the expected total drift per site, $\delta$, belongs to the interval $[-1,1]$. We show that if $|\delta|<1$ then the diffusively scaled ERW under the averaged measure converges to a $(\delta,-\delta)$-perturbed Brownian motion. In the boundary case, $|\delta|=1$, the space scaling has to be adjusted by an extra logarithmic term, and the weak limit of ERW happens to be a constant multiple of the running maximum of the standard Brownian motion, a transient process.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Fields Institute for Research in Mathematical Sciences; NSF; PSC CUNY; Simons Foundation
7.	Date	(YYYY-MM-DD)	2012-08-09
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2213
10.	Identifier	Digital Object Identifier	10.1214/ECP.v17-2213
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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